QCAA Maths Methods Paper 1 Trigonometry Mini Test 1
External Assessment Paper 1 — Technology-free
Number of marks: 8
Perusal time: 1 minute
Writing time: 12 minutes
Section 1
Instructions
• This section has 10 questions and is worth 10 marks.
• Use a 2B pencil to fill in the A, B, C or D answer bubble completely.
• Choose the best answer for Questions 1 10.
• If you change your mind or make a mistake, use an eraser to remove your response and fill in the new answer bubble completely.
A circle with radius \(r\) and internal angle \(\theta\) has a shaded segment as shown.
If \(\theta\) is in radians, the area of the shaded segment is
- (A) \(\frac{r^2}{2} \left( \frac{\theta\pi}{180} - \sin(\theta) \right)\)
- (B) \(\frac{r^2}{2} (\theta - \sin(\theta))\)
- (C) \(\frac{r^2}{4} \left( \frac{\theta\pi}{90} - 1 \right)\)
- (D) \(\frac{r^2}{2} (\theta - 1)\)
Section 2
Instructions
• Write using black or blue pen.
• Questions worth more than one mark require mathematical reasoning and/or working to be shown to support answers.
• If you need more space for a response, use the additional pages at the back of this book.
– On the additional pages, write the question number you are responding to.
– Cancel any incorrect response by ruling a single diagonal line through your work.
– Write the page number of your alternative/additional response, i.e. See page …
– If you do not do this, your original response will be marked.
• This section has nine questions and is worth 45 marks.
In the isosceles triangle \(ABC\), angle \(C\) is \(120^\circ\) and side \(a\) is 4 cm.
a) Draw the triangle, indicating all given information. [1 mark]
Note: If you make a mistake in the diagram, cancel it by ruling a single diagonal line through your work and use the additional diagram on page 17 of this question and response book.
b) Calculate the area of the triangle in cm\(^2\). (Give your answer in simplest form.) [3 marks]
Determine the area of the triangle shown.
END OF PAPER
